The equation of a line is `3x+4y-10=0`. Convert this equation into :
`(i)` slope-intercept
`(ii)` intercept
`(iii)` perpendicular form

Explanation

`(i) 3x+4y-10=0`
`implies 4y=-3x+10`
`implies y=-(3)/(4)x+(5)/(2)`
Comparing with `y=mx+c`
Slope `m=-(3)/(4)`, `y-` intercept `c=(5)/(2)`
`(ii) 3x+4y-10=0`
`implies 3x+4y=10`
`implies (3x)/(10)+(4y)/(10)=1`
`implies (x)/((10)/(3))+(y)/((5)/(2))=1`
Comparing with `(x)/(a)+(y)/(b)=1`
Intercept on `X`-axis `='a'=(10)/(3)` units.
Intercept on `Y`-axis `='b'=(5)/(2)` units.
`(iii) 3x+4y-10=0`
`implies 3x+4y=10`
(Taking constant term positive)
Divide both sides by `sqrt(3^(2)+4^(2))=5`
`(3)/(5)x+(4)/( 5)y=2`
Comparing with `x cos alpha+y sin alpha=p`
`cos alpha=(3)/(5)`, `sin alpha=(4)/(5)` and `p=2` units